Parameter Identification Of LTV System Based On Wavelet Method

Many structure damage detection methods have been developed based on atime-invariantdynamical systemthatisassumethestructuralphysicalparameters(such as stiffness, damping coefficients) are time-invariant. However, in fact, thephysical parameters and dynamical character of the structure duringthe occurrence ofdamage are time-varying, and the response signalbehaves a non-stationary character.Thus, it is generally recognized that the linear time-varying(LTV) model is moreappropriate and better than linear time-invariant(LTI) model to capture theinstantaneous dynamical behaviors. The identification of LTV system has beenreceivedincreasingattentionnowadays.Fourier Transform(FT) and Short Time Fourier Transform(STFT) can't satisfythe requirement of non-stationary signal analysis. With the multiresolution character,Wavelet Transform(WT) is widely applied in analysis of non-stationary signal andsolving partial differential equations. The approach to compute the correspondingwavelet coefficientsisintroducedinthispaper.An identification algorithm of physical parameters of the LTVdynamical systemis developed in this paper. The response and excitation signals are first decomposedusing the Daubechies wavelet scaling function. Then the differential vibrationequations of the time-varying system are transformed into simple linear equationsbased on the orthogonality of the scaling functions. The physical parameters can beidentified directly by solving the linear equations. The parameter identificationequationsofthreecases:single-degree-of-freedom(SDOF),multi-degree-of-freedom(MDOF) and a cantilever beam LTV system are developed. Numerical resultsdemonstrate the accuracy and the validity of the proposed method for identificationthe parameters of LTI system and smoothly, periodically and abruptly time-varyingparameters of LTV system. Using the free response of the system, the identificationprecision of the method on different scale is investigated and the method is alsoappliedto structuredamagedetection.The research is supported bythe National Natural Science Foundation of Chinaunder the contract number 10372041 and the Aeronautics Foundation under thecontractnumber 02B52013.